![Question 7(a). A string is wound around a uniform disc of mass M and radius R. The dise is released from rest with the string vertical and its top end tied to a fixed bar (Fig.4). Find 6 the tension in the string. (ii) the magnitude of acceleration of the centre of mass. (ii) the speed of the centre of mass of the disc after it has descended through the distance h. 2 121 121 Figure 4 Question 7(b). A wheel rotates from rest about a fixed axis through its centre of mass suclh that its angular displacement θ as a function of time t, is given by the following equation θ = bt, where b is a positive constant. If the moment of inertia of the wheel about the axis through it centre of mass is IcM, find (i) the work done by the net torque on the wheel in terms of lcw and Q when it has turned through an angle θ 14] (i) the angular speed of the wheel (in terms of θ ) when it has turned through an angle e 121](http://img.homeworklib.com/questions/9a9e2630-d1d8-11ea-a4a2-1f7803718a74.png?x-oss-process=image/resize,w_560)
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Question 7(a). A string is wound around a uniform disc of mass M and radius R....
A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and its top end tied to a fixed bar. See the figure below.
A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and its top end tied to a fixed bar. See the figure below. (Submit a file with a maximum size of 1 MB.) (a) Show that the tension in the string is one third of the weight of the disk. (b) Show that the magnitude of the acceleration of the center of mass is 2g/3. (c) Show that the...
A string is wrapped around a uniform cylinder of mass M and radius R as shown...
A string is wrapped around a uniform cylinder of mass M and radius R as shown in figure 4. The cylinder is released from rest with the string vertical and its top end tied to a fixed bar. a. Show that the tension in the string is one-third the weight of the cylinder. b. Show that the magnitude of the acceleration of the center of gravity is 2g/3. c. Show that the speed of the center of gravity is (4gl/3)^1/2...
A disk of uniform mass M and radius R (Icm = 1 / 2MR2) is tied...
A disk of uniform mass M and radius R (Icm = 1 / 2MR2) is tied to a rope that in turn is tied to the ceiling, as shown in figure 2. The mass is released from rest and its center of mass low with a constant acceleration of (Assume that there is friction between the string and the disc and therefore it does not slip.):
20.) A circular disc of mass M =500 gm and radius R = 20 cm is...
20.) A circular disc of mass M =500 gm and radius R = 20 cm is rotating about an axis perpendicular to it and passing through its centre. The initial angular speed of rotation of the disc is 30 rad/s. A bug of mass m = 25 gm which was originally on the disc at the rotating axis crawls outward and stops when it is 5 cm from the rim of the disc Calculate the new speed of rotation of...
Question 1. A uniform circular disc of mass m and radius r is pivoted at point...
Question 1. A uniform circular disc of mass m and radius r is pivoted at point 0, as shown in Figure 1. The disc is released from the position shown. Immediately after the release: (a) Obtain the angular acceleration of the disc in terms of r,1,g, and 0. [5 marks) [8 marks) Assuming r = 0.5 m and @ = 30° and using plot function in MATLAB: (b) Determine how the initial angular acceleration changes as I is varried from...
A bicycle wheel is mounted on a fixed, frictionless axle, with alight string wound around its rim. The wheel has moment...
A bicycle wheel is mounted on a fixed, frictionless axle, with alight string wound around its rim. The wheel has moment of inertia I=kmr2, where m is its mass, r is its radius, and k is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular velocity w0, when at time t=0 someone starts pulling the string with a force of magnitude F. Assume that the string does not slip on the wheel.Part ASuppose that after a certain time tL,...
A uniform disc with mass M and radius R = 0.10 m is mounted on a...
A uniform disc with mass M and radius R = 0.10 m is mounted on a frictionless, horizontal axle, as shown in the figure. The light cord wrapped around the disk is pulled so that it has a constant tension of T = 20.0 N. Starting from the rest, the disk performs a rotational motion with a constant angular acceleration a = 2 rad/s2 Find mass M of the disk. (Note that the moment of inertia of the disk is...
A 3-kg mass is attached to a light, thin string that is wound around a uniform...
A 3-kg mass is attached to a light, thin string that is wound around a uniform cylinder with a mass of 4 kg and a radius of 4 cm. The 3-kg mass is released from rest and the cylinder turns without friction as the 3-kg mass falls. a) What is the speed of the 3-kg mass after it falls 40 cm? the angular speed of the cylinder after the mass falls 40 cm?
A uniform disc of radius 30 cm and mass 12 kg is pivoted so that it...
A uniform disc of radius 30 cm and mass 12 kg is pivoted so that it is free to rotate about an axis through its center. A string wrapped around the disc is pulled with a force of 80 N. What is the angular velocity of the disc after 5 s ?
A thin light string is wrapped around a solid uniform disk of mass M and radius...
A thin light string is wrapped around a solid uniform disk of mass M and radius R, mounted as shown. The loose end of the string is attached to the axle of a solid uniform disc of mass m and the same radius r which is can roll down without slipping down an inclined plane that makes angle θ with the horizontal. Find the acceleration a of the rolling disc. Neglect friction in the axle of the pulley. a =...
A string is wrapped around a uniform cylinder of mass M and radius R as shown in figure 4. The cylinder is released from rest with the string vertical and its top end tied to a fixed bar. a. Show that the tension in the string is one-third the weight of the cylinder. b. Show that the magnitude of the acceleration of the center of gravity is 2g/3. c. Show that the speed of the center of gravity is (4gl/3)^1/2...
20.) A circular disc of mass M =500 gm and radius R = 20 cm is rotating about an axis perpendicular to it and passing through its centre. The initial angular speed of rotation of the disc is 30 rad/s. A bug of mass m = 25 gm which was originally on the disc at the rotating axis crawls outward and stops when it is 5 cm from the rim of the disc Calculate the new speed of rotation of...
Question 1. A uniform circular disc of mass m and radius r is pivoted at point 0, as shown in Figure 1. The disc is released from the position shown. Immediately after the release: (a) Obtain the angular acceleration of the disc in terms of r,1,g, and 0. [5 marks) [8 marks) Assuming r = 0.5 m and @ = 30° and using plot function in MATLAB: (b) Determine how the initial angular acceleration changes as I is varried from...
A uniform disc with mass M and radius R = 0.10 m is mounted on a frictionless, horizontal axle, as shown in the figure. The light cord wrapped around the disk is pulled so that it has a constant tension of T = 20.0 N. Starting from the rest, the disk performs a rotational motion with a constant angular acceleration a = 2 rad/s2 Find mass M of the disk. (Note that the moment of inertia of the disk is...
A 3-kg mass is attached to a light, thin string that is wound around a uniform cylinder with a mass of 4 kg and a radius of 4 cm. The 3-kg mass is released from rest and the cylinder turns without friction as the 3-kg mass falls. a) What is the speed of the 3-kg mass after it falls 40 cm? the angular speed of the cylinder after the mass falls 40 cm?
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